## Multiple positive solutions of nonlinear third-order BVP for a class of $$p$$-Laplacian dynamic equations on time scales.(English)Zbl 1165.34321

### MSC:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 39A10 Additive difference equations
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### References:

 [1] Agarwal, R.P.; Bohner, M.; Rehak, P., Half-linear dynamic equations, (), 1-57 · Zbl 1056.34049 [2] Agarwal, R.P.; O’Regan, D., Nonlinear boundary value problems on time scales, Nonlinear anal., 44, 527-535, (2001) · Zbl 0995.34016 [3] Anderson, D.R.; Avery, R.; Henderson, J., Existence of solutions for a one-dimensional $$p$$-Laplacian on time scales, J. difference equ. appl., 10, 889-896, (2004) · Zbl 1058.39010 [4] Anderson, D.R.; Gnseinov, G.Sh.; Hoffacker, J., Higher-order self-adjoint boundary-value problems on time scales, J. comput. appl. math., 194, 309-342, (2006) · Zbl 1098.39008 [5] Atici, F.M.; Gnseinov, G.Sh., On green’n functions and positive solutions for boundary value problems on time scales, J. comput. anal. math., 141, 75-99, (2002) · Zbl 1007.34025 [6] Aulbach, B.; Neidhart, L., Integration on measure chain, (), 239-252 · Zbl 1083.26005 [7] Bai, C.Z.; Fang, J.X., Existence of multiple positive solutions for nonlinear $$m$$ point boundary value problems, J. math. anal. appl., 281, 76-85, (2003) · Zbl 1030.34026 [8] Bohner, M.; Peterson, A., Dynamic equations on time scales: an introduction with applications, (2001), Birkhäuser Boston, Cambridge, MA · Zbl 0978.39001 [9] Bohner, M.; Peterson, A., Advances in dynamic equations on time scales, (2003), Birkhäuser Boston, Cambridge, MA · Zbl 1025.34001 [10] Erbe, L.H.; Peterson, A., Positive solutions for nonlinear differential equation on a measure chain, Math. comput. modelling, 32, 571-585, (2000) · Zbl 0963.34020 [11] Grossinho, M.R.; Minhós, F.M.; Santos, A.I., Existence results for a third-order ODE with nonlinear boundary conditions in presence of a sign-type Nagumo control, J. math. anal. appl., 309, 271-283, (2005) · Zbl 1089.34017 [12] Guo, D.J.; Sun, J.X., Topological degree’s computation and application, J. math. res. exposition, 8, 3, 469-480, (1988), (in Chinese) [13] Hao, Z.C.; Liang, J.; Xiao, T.J., Existence results for time scale boundary value problem, J. comput. appl. math., 197, 156-168, (2006) · Zbl 1107.34018 [14] He, Z.M., Triple positive solutions of boundary value problems for $$p$$-Laplacian dynamic equations on time scales, J. math. anal. appl., 321, 911-920, (2006) · Zbl 1103.34012 [15] Li, S.H., Positive solutions of nonlinear singular third-order two-point boundary value problem, J. math. anal. appl., 323, 413-425, (2006) · Zbl 1107.34019 [16] Ma, D.; Du, Z.; Ge, W., Existence and iteration of monotone positive solutions for multipoint boundary value problem with $$p$$-Laplacian operator, Comput. math. appl., 50, 729-739, (2005) · Zbl 1095.34009 [17] Ma, R.Y., Existence of solutions of nonlinear $$m$$-point boundary value problem, J. math. anal. appl., 256, 556-567, (2001) · Zbl 0988.34009 [18] Mao, A.M.; Luan, S.X.; Ding, Y.H., On the existence of positive solutions for a class of singular boundary value problems, J. math. appl., 298, 57-72, (2004) · Zbl 1073.34019 [19] Su, H.; Wang, B.; Wei, Z., Positive solutions of four-point boundary value problems for four-order $$p$$-Laplacian dynamic equations on time scales, Electron. J. differential equations, 78, 1-13, (2006) · Zbl 1117.34028 [20] Su, H.; Wei, Z.; Xu, F., The existence of countably many positive solutions for a system of nonlinear singular boundary value problems with the $$p$$-Laplacian operator, J. math. anal. appl., 325, 319-332, (2007) · Zbl 1108.34015 [21] Sun, H.R.; Li, W.T., Existence theory for positive solutions to one-dimensional $$p$$-Laplacian boundary value problems on time scales, J. differential equations, 240, 217-248, (2007) · Zbl 1139.34047 [22] Sun, H.R.; Li, W.T., Multiple positive solutions for $$p$$-Laplacian $$m$$-point boundary value problems on time scales, Appl. math. comput., 182, 478-491, (2006) · Zbl 1126.34019 [23] Sun, Y.P., Positive solutions of singular third-order three-point boundary value problem, J. math. anal. appl., 306, 589-603, (2005) · Zbl 1074.34028 [24] Zhou, C.L.; Ma, D.X., Existence and iteration of positive solutions for a generalized right-focal boundary value problem with $$p$$-Laplacian operator, J. math. anal. appl., 324, 409-424, (2006) · Zbl 1115.34029 [25] Minhós, F., On some third order nonlinear boundary value problems: existence, location and multiplicity results, J. math. anal. appl., 339-2, 1342-1353, (2008) · Zbl 1144.34009 [26] Guo, D.; Lakshmikantham, V., Nonlinear problems in abstract cones, (1988), Academic Press San Diego · Zbl 0661.47045
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